Electron. J. Diff. Eqns., Vol. 2007(2007), No. 95, pp. 1-9.

Three positive solutions for p-Laplacian functional dynamic equations on time scales

Da-Bin Wang

In this paper, we establish the existence of three positive solutions to the following p-Laplacian functional dynamic equation on time scales,
 [ \Phi _p(u^{\Delta }(t))] ^{\nabla}+a(t)f(u(t),u(\mu (t)))=0,\quad
 t\in (0,T)_{T}, \cr
 u_0(t)=\varphi (t),\quad t\in [-r,0] _{T},\cr
 u(0)-B_0(u^{\Delta }(\eta ))=0,\quad u^{\Delta }(T)=0,.
using the fixed-point theorem due to Avery and Peterson [8]. An example is given to illustrate the main result.

Submitted May 17, 2007. Published June 29, 2007.
Math Subject Classifications: 39A10, 34B15.
Key Words: Time scale; p-Laplacian functional dynamic equation; boundary value problem; positive solution; fixed point.

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Da-Bin Wang
Department of Applied Mathematics
Lanzhou University of Technology
Lanzhou, Gansu, 730050, China
email: wangdb@lut.cn

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